How to Make It
Bring a medium saucepan of water to a boil. Add the peas and cook just until tender, about 5 minutes. Using a slotted spoon, transfer the peas to a bowl of cold water. Drain well.
Return the water in the saucepan to a boil and add the tomatoes. Cook for 10 seconds, then transfer to a bowl of cold water. Peel the tomatoes and halve them horizontally. Working over a strainer set over a bowl, scrape out the seeds with a spoon. Press on the seeds to extract all the juice; discard the seeds. Finely chop 1 of the tomatoes and add it to the juice. Cut the other tomato into 3/4-inch pieces.
Heat 1 tablespoon of the oil in a large skillet. Add the corn, sliced scallions, artichoke, garlic and peas and cook over moderate heat, stirring, until softened slightly. Add the chicken stock and asparagus and cook until the liquid has reduced by half, about 5 minutes. Stir in the finely chopped tomato with its juice and a pinch each of salt and pepper. Cook over moderate heat until the liquid is nearly evaporated, about 3 minutes. Off the heat, stir in the basil, the scallion greens and the remaining tomato.
In a large pot of boiling salted water, cook the Petal-Printed Pasta, stirring occasionally, until al dente, about 5 minutes. Drain well. Spoon the ragout into 8 warmed shallow soup plates and top with the pasta. Lightly brush the pasta with the remaining 1/2 tablespoon of olive oil. Sprinkle with the Parmigiano-Reggiano and serve at once.